# Lotka-Sharpe Neural Operators for Control of Population PDEs

arXiv: https://arxiv.org/abs/2604.03892 · HTML: https://mlsanity.com/paper/2604.03892/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 31 references that are in the map.
- First posted on arXiv 4 Apr 2026.

## Builds on (most cited first, 16 of 16)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Nonlocality and Nonlinearity Implies Universality in Operator Learning](https://mlsanity.com/paper/2304.13221/) (2023)
- [Neural Operators for Bypassing Gain and Control Computations in PDE Backstepping](https://mlsanity.com/paper/2302.14265/) (2023)
- [Neural Operators of Backstepping Controller and Observer Gain Functions for Reaction-Diffusion PDEs](https://mlsanity.com/paper/2303.10506/) (2023)
- [Gain Scheduling with a Neural Operator for a Transport PDE with Nonlinear Recirculation](https://mlsanity.com/paper/2401.02511/) (2024)
- [Adaptive Neural-Operator Backstepping Control of a Benchmark Hyperbolic PDE](https://mlsanity.com/paper/2401.07862/) (2024)
- [Backstepping Neural Operators for 2× 2 Hyperbolic PDEs](https://mlsanity.com/paper/2312.16762/) (2023)
- [Stabilization of nonlinear systems with unknown delays via delay-adaptive neural operator approximate predictors](https://mlsanity.com/paper/2509.26443/) (2025)
- [Stability of Integral Delay Equations and Stabilization of Age-Structured Models](https://mlsanity.com/paper/1609.09437/) (2016)
- [Yield Trajectory Tracking for Hyperbolic Age-Structured Population Systems](https://mlsanity.com/paper/1701.05793/) (2017)
- [Stabilization of Age-Structured Chemostat Hyperbolic PDE with Actuator Dynamics](https://mlsanity.com/paper/2306.14078/) (2023)
- [Stabilization of Predator-Prey Age-Structured Hyperbolic PDE when Harvesting both Species is Inevitable](https://mlsanity.com/paper/2410.06823/) (2024)
- [Neural Operators for Adaptive Control of Traffic Flow Models](https://mlsanity.com/paper/2505.07353/) (2025)
- [Stabilization of Age-Structured Competing Populations](https://mlsanity.com/paper/2507.23013/) (2025)
- [The Age-Structured Chemostat with Substrate Dynamics as a Control System](https://mlsanity.com/paper/2511.09963/) (2025)

## Abstract (arXiv)

Age-structured predator-prey integro-partial differential equations provide models of interacting populations in ecology, epidemiology, and biotechnology. A key challenge in feedback design for these systems is the scalar zeta, defined implicitly by the Lotka-Sharpe nonlinear integral condition, as a mapping from fertility and mortality rates to zeta. To solve this challenge with operator learning, we first prove that the Lotka-Sharpe operator is Lipschitz continuous, guaranteeing the existence of arbitrarily accurate neural operator approximations over a compact set of fertility and mortality functions. We then show that the resulting approximate feedback law preserves semi-global practical asymptotic stability under propagation of the operator approximation error through various other nonlinear operators, all the way through to the control input. In the numerical results, not only do we learn ``once-and-for-all'' the canonical Lotka-Sharpe (LS) operator, and thus make it available for future uses in control of other age-structured population interconnections, but we demonstrate the online usage of the neural LS operator under estimation of the fertility and mortality functions.